A framework is presented for a computational theory of probabilistic argument. The Probabilistic Reasoning Environment encodes knowledge at three levels. At the deepest level are a set of schemata encoding the system's domain knowledge. This knowledge is used to build a set of second-level arguments, which are structured for efficient recapture of the knowledge used to construct them. Finally, at the top level is a Bayesian network constructed from the arguments. The system is designed to facilitate not just propagation of beliefs and assimilation of evidence, but also the dynamic process of constructing a belief network, evaluating its adequacy, and revising it when necessary.

While concept-based methods for information retrieval can provide improved performance over more conventional techniques, they require large amounts of effort to acquire the concepts and their qualitative and quantitative relationships. This paper discusses an architecture for probabilistic concept-based information retrieval which addresses the knowledge acquisition problem. The architecture makes use of the probabilistic networks technology for representing and reasoning about concepts and includes a knowledge acquisition component which partially automates the construction of concept knowledge bases from data. We describe two experiments that apply the architecture to the task of retrieving documents about terrorism from a set of documents from the Reuters news service. The experiments provide positive evidence that the architecture design is feasible and that there are advantages to concept-based methods.

We define a new notion of conditional belief, which plays the same role for Dempster-Shafer belief functions as conditional probability does for probability functions. Our definition is different from the standard definition given by Dempster, and avoids many of the well-known problems of that definition. Just as the conditional probability Pr (lB) is a probability function which is the result of conditioning on B being true, so too our conditional belief function Bel (lB) is a belief function which is the result of conditioning on B being true. We define the conditional belief as the lower envelope (that is, the inf) of a family of conditional probability functions, and provide a closed form expression for it. An alternate way of understanding our definition of conditional belief is provided by considering ideas from an earlier paper [Fagin and Halpern, 1989], where we connect belief functions with inner measures. In particular, we show here how to extend the definition of conditional probability to non measurable sets, in order to get notions of inner and outer conditional probabilities, which can be viewed as best approximations to the true conditional probability, given our lack of information. Our definition of conditional belief turns out to be an exact analogue of our definition of inner conditional probability.

This paper discusses how a measure of uncertainty representing a state of knowledge can be updated when a new information, which may be pervaded with uncertainty, becomes available. This problem is considered in various framework, namely: Shafer's evidence theory, Zadeh's possibility theory, Spohn's theory of epistemic states. In the two first cases, analogues of Jeffrey's rule of conditioning are introduced and discussed. The relations between Spohn's model and possibility theory are emphasized and Spohn's updating rule is contrasted with the Jeffrey-like rule of conditioning in possibility theory. Recent results by Shenoy on the combination of ordinal conditional functions are reinterpreted in the language of possibility theory. It is shown that Shenoy's combination rule has a well-known possibilistic counterpart.

Cutset conditioning and clique-tree propagation are two popular methods for performing exact probabilistic inference in Bayesian belief networks. Cutset conditioning is based on decomposition of a subset of network nodes, whereas clique-tree propagation depends on aggregation of nodes. We describe a means to combine cutset conditioning and clique- tree propagation in an approach called aggregation after decomposition (AD). We discuss the application of the AD method in the Pathfinder system, a medical expert system that offers assistance with diagnosis in hematopathology.

We introduce a new heuristic algorithm for the problem of finding minimum size loop cutsets in multiply connected belief networks. We compare this algorithm to that proposed in [Suemmondt and Cooper, 1988]. We provide lower bounds on the performance of these algorithms with respect to one another and with respect to optimal. We demonstrate that no heuristic algorithm for this problem cam be guaranteed to produce loop cutsets within a constant difference from optimal. We discuss experimental results based on randomly generated networks, and discuss future work and open questions.

This paper analyzes the circumstances under which Bayesian networks can be pruned in order to reduce computational complexity without altering the computation for variables of interest. Given a problem instance which consists of a query and evidence for a set of nodes in the network, it is possible to delete portions of the network which do not participate in the computation for the query. Savings in computational complexity can be large when the original network is not singly connected. Results analogous to those described in this paper have been derived before [Geiger, Verma, and Pearl 89, Shachter 88] but the implications for reducing complexity of the computations in Bayesian networks have not been stated explicitly. We show how a preprocessing step can be used to prune a Bayesian network prior to using standard algorithms to solve a given problem instance. We also show how our results can be used in a parallel distributed implementation in order to achieve greater savings. We define a computationally equivalent subgraph of a Bayesian network. The algorithm developed in [Geiger, Verma, and Pearl 89] is modified to construct the subgraphs described in this paper with O(e) complexity, where e is the number of edges in the Bayesian network. Finally, we define a minimal computationally equivalent subgraph and prove that the subgraphs described are minimal.

In this paper, optimum decomposition of belief networks is discussed. Some methods of decomposition are examined and a new method - the method of Minimum Total Number of States (MTNS) - is proposed. The problem of optimum belief network decomposition under our framework, as under all the other frameworks, is shown to be NP-hard. According to the computational complexity analysis, an algorithm of belief network decomposition is proposed in (Wee, 1990a) based on simulated annealing.

In recent years, there have been intense research efforts to develop efficient methods for probabilistic inference in probabilistic influence diagrams or belief networks. Many people have concluded that the best methods are those based on undirected graph structures, and that those methods are inherently superior to those based on node reduction operations on the influence diagram. We show here that these two approaches are essentially the same, since they are explicitly or implicity building and operating on the same underlying graphical structures. In this paper we examine those graphical structures and show how this insight can lead to an improved class of directed reduction methods.

IDEAL (Influence Diagram Evaluation and Analysis in Lisp) is a software environment for creation and evaluation of belief networks and influence diagrams. IDEAL is primarily a research tool and provides an implementation of many of the latest developments in belief network and influence diagram evaluation in a unified framework. This paper describes IDEAL and some lessons learned during its development.